A Fiber-coupled Scanning Magnetometer with Nitrogen-Vacancy Spins in a Diamond Nanobeam

TL;DR

This paper introduces a fiber-coupled diamond nanobeam sensor with nitrogen-vacancy spins for high-efficiency optical magnetic imaging, suitable for challenging environments like cryostats or biological systems.

Contribution

It presents a novel scanning-NV sensor design that integrates a diamond nanobeam with tapered optical fiber for efficient optical access and magnetic sensing.

Findings

Demonstrated through-fiber optically interrogated electron spin resonance.

Achieved proof-of-principle magnetometry by imaging spin waves.

Sensor design enables operation in challenging environments.

Abstract

Magnetic imaging with nitrogen-vacancy (NV) spins in diamond is becoming an established tool for studying nanoscale physics in condensed matter systems. However, the optical access required for NV spin readout remains an important hurdle for operation in challenging environments such as millikelvin cryostats or biological systems. Here, we demonstrate a scanning-NV sensor consisting of a diamond nanobeam that is optically coupled to a tapered optical fiber. This nanobeam sensor combines a natural scanning-probe geometry with high-efficiency through-fiber optical excitation and readout of the NV spins. We demonstrate through-fiber optically interrogated electron spin resonance and proof-of-principle magnetometry operation by imaging spin waves in an yttrium-iron-garnet thin film. Our scanning-nanobeam sensor can be combined with nanophotonic structuring to control the light-matter interaction strength, and has potential for applications that benefit from all-fiber sensor access such as millikelvin systems.

Equations

$$\Gamma =\eta N\gamma \frac{P}{P+P_{\mathrm{sat}}}+{\Gamma }_{\mathrm{dark}}.$$

$$\Gamma ={\eta }_{\mathrm{f}}{\eta }_{\mathrm{D}}{\eta }_{\mathrm{nf}}^2\frac{{\sigma }_{\mathrm{NV}}{N}_{\mathrm{mode}}}{{\sigma }_{\mathrm{mode}}}\frac{P}{\hslash \omega }$$

Full text

QN] Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands \alsoaffiliation[3me] Department of Precision and Microsystems Engineering, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The Netherlands

QN] Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands

QN] Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands

Qutech] QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands

QN] Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands

Qutech] QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands

QN] Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands \alsoaffiliation[3me] Department of Precision and Microsystems Engineering, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The Netherlands

QN] Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands

\abbreviationsIR,NMR,UV

1 Introduction

The nitrogen-vacancy (NV) lattice defect in diamond has emerged as a powerful magnetic-field sensor. High-fidelity microwave control and optical readout of the NV spin 1, 2, 3 over a wide range of conditions has enabled applications in condensed matter physics 4, chemistry 5, biology 6, 7 and geoscience 8. In particular, scanning-probe magnetometry based on individual NV spins in diamond nanotips has provided imaging of spins and currents in materials with spatial resolution down to $\sim$50\text{,}\mathrm{nm}$$ 9, 10, 11.

An important challenge for the application of scanning-probe NV magnetometry in advanced environments such as millikelvin cryostats is the required optical access to the NV spins. Free-space optical access leads to additional heat load and increased complexity of cryostat design. A potential way to preclude the need for free-space optical access is to realize fiber-based scanning-NV sensors 12, 13. Here, we demonstrate a new scanning-NV sensor based on a tapered diamond nanobeam that is optically coupled to, and manipulated with a tapered optical fiber. Such fiber-based NV nanobeam sensors could facilitate implementation in low-temperature setups, while benefiting from the potentially near-perfect optical coupling efficiency between fiber and nanobeam 14, 15, 16. Moreover, nanobeams are excellently suited for nanophotonic structuring 17, 18, which could enable high-efficiency, resonant optical addressing of embedded NV centers or other group-IV color centers19 by incorporating photonic crystals.

We fabricate the diamond nanobeams using nanofabrication recipes developed in Refs. 18, 20, 21, 22. The key advance we present here is the ability to break off and attach individual tapered diamond nanobeams to nanoscale-tapered optical fibers and use these nanobeam sensors for scanning NV magnetometry (fig. 1(a)). We break a beam off the bulk diamond by pushing on it with the fiber, after which the beam and the fiber remain attached, presumably by van der Waals forces. We found it crucial to create long ($\sim$40\text{,}\mathrm{\SIUnitSymbolMicro m}) nanobeams to provide a sufficient lever arm that prevents damaging the glass fiber tip. The use of $\sim$70\text{\,}\mathrm{nm} wide bridges between the nanobeam and bulk diamond (fig. 2(b)) enables easy breaking. As a proof of principle, we demonstrate through-fiber optical interrogation of an NV-nanobeam sensor, characterize its photon collection efficiency, and demonstrate its imaging capability by visualizing spin waves in a thin film of yttrium-iron-garnet (YIG) 11, 23.

2 Results and Discussion

Efficient optical coupling to the fiber requires tapered diamond nanobeams with nanoscale widths 15. We fabricate these beams out of a single-crystal diamond chip using the procedure demonstrated in Ref. 22 (fig. 2). We first deposit a $200\text{\,}\mathrm{nm}$-thick $\mathrm{Si_{3}N_{4}}$ mask onto the diamond using plasma-enhanced chemical vapor deposition (PECVD). We then use e-beam lithography and reactive ion etching (RIE) with a $\mathrm{CHF_{3}/O_{2}}$ plasma to pattern the beams and their holding bars (“tethers”) on the $\mathrm{Si_{3}N_{4}}$ hard mask. An anisotropic, inductively-coupled plasma (ICP) RIE with O2 transfers the patterns from the hard mask to the diamond substrate (fig. 2(b)). Using atomic layer deposition (ALD) to deposit $20\text{\,}\mathrm{n}\mathrm{m}$ of $\mathrm{Al_{2}O_{3}}$ 18, we create a conformal layer that protects the vertical sidewalls during the subsequent undercut. An anisotropic ICP-RIE with $\mathrm{BCl_{3}/Cl_{2}}$ removes the $\mathrm{Al_{2}O_{3}}$ from the horizontal diamond surfaces while leaving the vertical beam sidewalls protected. Finally, we undercut the nanobeams with a quasi-isotropic $\mathrm{O_{2}}$ ICP-RIE and remove the masks with hydrofluoric acid (HF), leaving free-hanging diamond nanobeams (fig. 2(c)).

To couple the nanobeams to a tapered optical fiber (S630-HP, tapered by HF pulling, see methods), we mount the nanobeam chip on a 3-axis slip-stick positioner (Mechonics MX-35). Monitoring through a microscope objective (Mitutoyo M Plan Apo HR 50$\times$), we push the fiber against the nanobeam by moving the stage perpendicularly to the beam until the connection point breaks and the nanobeam sticks to the fiber. The sticking is presumably due to van der Waals force. The process and end result are illustrated in fig. 3.

Compared to similar strategies of picking up nanophotonic structures made from other materials, such as Si or SiN 24, 25, 26, the main challenge lies in the significantly larger yield strength of diamond compared to glass27. Also, single crystal diamond on the nanoscale is known to exhibit large elastic deformation before fracturing when pressure is applied 28, as we also observe while pushing on the beam with the fiber in fig. 3(b). The resulting abrupt motion when the beam breaks makes it challenging to stick the beam to the optical fiber. To overcome this challenge, we found it crucial to design beams that are at least $30\text{\,}\mathrm{\SIUnitSymbolMicro m}$ in length. Furthermore, we minimize the width of the tether by fabricating an array of devices with varying tether widths, and use the beams with the thinnest tethers that survived the fabrication process. Furthermore, the area of the open region around the beam should be large enough (in our design 70\text{\,}\mathrm{\SIUnitSymbolMicro m}$\times$40\text{\,}\mathrm{\SIUnitSymbolMicro m}) to allow for the beam displacement during the breaking process. With these design implementations, we are able to apply a large enough torque on the tether to break the nanobeam off the bulk with a tapered optical fiber, and couple the beam to the fiber in the same process. We find tether widths of 60-80 nm to be optimal, where around 60% of the beams remain attached to the bulk after the undercut and subsequent acid cleaning, and can be picked up by the tapered fiber with a success rate of 40% (four out of ten beams).

We demonstrate through-fiber optical excitation and readout of an ensemble of NV centers in a diamond nanobeam using the setup depicted in Fig. 1(b). Our nanobeams (fabricated using Element-six DNV-B14 diamond) have an estimated NV concentration of $4.5\text{\,}\mathrm{p}\mathrm{p}\mathrm{m}$ 29, corresponding to $N\approx 4.5\times 10^{6}$ NVs per nanobeam ($40\text{\,}\mathrm{\SIUnitSymbolMicro m}$ long, maximum cross section $0.5\times$0.5\text{,}\mathrm{\SIUnitSymbolMicro m}$^{2}$ and tapered down to $\sim 0.1\times$0.5\text{,}\mathrm{\SIUnitSymbolMicro m}$^{2}$ over $30\text{\,}\mathrm{\SIUnitSymbolMicro m}$ length). We apply microwaves (Windfreak SynthHD) through a co-planar waveguide to drive the electron-spin resonance (ESR) of the NV centers. Figure 3(d) shows a characteristic ESR spectrum measured through-fiber from our device, where the dips result from the microwave-driven transition between NV spin states $|m_{S}=0\rangle\rightarrow|m_{S}=\pm 1\rangle$. Due to the high NV density, we record the ESR signal with only $30\text{\,}\mathrm{nW}$ of excitation power. Comparing the photoluminescence measured in fig. 3(d) to a control measurement of the fiber autoluminescence (fig. 3(f)) shows that the signal is dominated by the NV photoluminescence (signal to background ratio: $8\times 10^{3}$) because of the high NV concentration in the nanobeam. By normalizing the photon count in fig. 3(d) to the total number of NVs $N$, we estimate the collected photoluminescence rate of a single NV center to be $\Gamma_{\mathrm{NV}}/N=$8.1\text{,}{\mathrm{s}}^{-1}\text{,}{\mathrm{\SIUnitSymbolMicro W}}^{-1}$\ll\Gamma_{\mathrm{fiber}}$. Therefore in order to achieve efficient single NV readout where $\Gamma_{\mathrm{NV}}/N\sim\Gamma_{\mathrm{fiber}}$, further effort is needed on both reducing the fiber autoluminescence and increasing the NV photon collection efficiency.

To estimate the photon coupling efficiency of the nanobeam-fiber interface $\eta_{\mathrm{nf}}$, we use two approaches. In the first, we characterize the saturation of the NV photoluminescence as a function of the optical excitation power $P$. Assuming a simple two-level model for the NV photodynamics, the NV photoluminescence is limited by the NV’s spontaneous emission rate $\gamma=$1/(13 ns) 30. As such, the photon count rate $\Gamma$ detected by our avalanche photodiode (APD, Laser Component COUNT-500N-FC) can be described by:

[TABLE]

Here, $\eta$ is the fraction of total number of photons emitted by the NVs that is detected by our APD, $P_{\mathrm{sat}}$ is the optical saturation power 31, and $\Gamma_{\mathrm{dark}}$ is a power-independent background rate (including e.g. APD dark counts). Because of the strong NV luminescence (fig. 3(e),(f)), we can omit the contribution of fiber autoluminescence and fit eq. 1 to the data in fig. 3(e). We extract $\eta=5.0(2)\times 10^{-10}$. Writing $\eta=\eta_{\mathrm{ND}}\eta_{\mathrm{D}}\eta_{\mathrm{nf}}$, where $\eta_{\mathrm{ND}}=1.6\times 10^{-7}$ is the neutral-density (ND) filtering factor and $\eta_{\mathrm{D}}=3.5\times 10^{-2}$ is the optical efficiency of the other parts of our setup (characterized separately, see SI), we extract the photon coupling efficiency at the fiber-nanobeam interface $\eta_{\mathrm{nf}}=8.6(4)$%. We note that the relatively small error here derives from the fit uncertainty of $\eta$. However, systematic uncertainties, such as the potential influence of two-photon-induced ionization of the NV centers to the neutral charge state, which would affect the detected photon rate due to the different spectrum of NV0 centers 32, 33 are likely to play a more important role. We therefore use a second approach to estimate $\eta_{\mathrm{nf}}$.

In the second approach, we estimate $\eta_{\mathrm{nf}}$ from the detected NV photoluminescence using a literature value for the NV’s absorption cross section $\sigma_{\mathrm{NV}}=3.1(8)\times 10^{-21}$ m2 for 532 nm laser excitation 34. Far below optical saturation, the detected NV photoluminescence is given by (see SI for detailed explanation)

[TABLE]

where $\sigma_{\mathrm{mode}}$ is the cross-sectional area of the optical mode in the nanobeam, $N_{\mathrm{mode}}$ is the number of NV centers within the optical mode volume, $\eta_{\mathrm{f}}$ is the coupling efficiency of the excitation laser into the fiber, $\omega$ is the frequency of our 532 nm laser and $\hbar$ is Planck’s constant. Furthermore, we assumed that the coupling of the green laser from the fiber into the nanobeam is also given by $\eta_{\mathrm{nf}}$. In contrast with the first approach, this approach does not require saturating the NV photoluminescence response and can thus be conducted at very low (nW) laser power. This reduces the potential influence of two-photon-induced ionization of the NV centers to the neutral charge state 32, 33. Assuming the mode is perfectly confined within the nanobeam, we take $N_{\mathrm{mode}}/\sigma_{\mathrm{mode}}\approx N/\sigma_{\mathrm{beam}}$ where $\sigma_{\mathrm{beam}}=$0.25\text{,}{\mathrm{\SIUnitSymbolMicro m}}^{2} is the cross-sectional area of the nanobeam. From the measured $\Gamma=$1.1\text{\times}{10}^{6}\text{\,}{\mathrm{s}}^{-1} at $P=$30\text{,}\mathrm{n}\mathrm{W}$$, we extract $\eta_{\mathrm{nf}}=14(4)$%, similar to the value found using the first approach.

We expect the found values for $\eta_{\mathrm{nf}}$ to be conservative estimates of the nanobeam-fiber coupling efficiencies due to the assumptions that all NV-emitted photons are radiated into the beam and towards the nanobeam-fiber interface, and because our two-level model neglects the non-radiative decay path via the singlet state that reduces the total photon emission rate 35. Compared to the state-of-the-art $\eta_{\mathrm{nf}}>90\%$ reported in Refs. 15, 16 for single-wavelength readout, an important difference in our device is the wide-band spectrum (bandwidth $\sim$200\text{,}\mathrm{nm}$$) of the collected NV photoluminescence. Also, the precise alignment of the fiber tip required to optimize the coupling efficiency is affected by the abrupt motion of the nanobeam when the tether breaks; From a through-fiber measurement of the NV photoluminescence of a beam that is still attached to the bulk diamond, we estimate using the absorption cross-section that $\eta_{\mathrm{nf,0}}=31(8)$% before breaking off the beam. Other factors that reduce the efficiency include the roughness on the sidewalls and bottom side of the nanobeams, which can be improved by optimizing the fabrication process, for instance by ion-based polishing of the nanobeam sidewall 36 or improved diamond etching.

Considering the above, our estimated nanobeam-fiber coupling efficiency is remarkably high, paving the way for high-efficiency, ensemble-based NV sensing. However, the fiber autoluminescence would still exceed the single-NV photoluminescence by about an order of magnitude even in the limit $\eta_{\mathrm{nf}}\rightarrow 1$ (according to eq. 2, $\Gamma_{\mathrm{NV,max}}/N=$4.1\text{\times}{10}^{2}\text{,}{\mathrm{s}}^{-1}\text{,}{\mathrm{\SIUnitSymbolMicro W}}^{-1}$$). This indicates that single-NV sensing will only be possible if the fiber autoluminescence can be reduced, for example by incorporating hollow-core photonic crystal fibers 37 that produce less fluorescence.

To demonstrate the imaging capability of our fiber-coupled nanobeam sensor, we use it to image spin waves – the wave-like excitations of spins in a magnetic material 38 – in a $\sim$250\text{,}\mathrm{nm}-thick film of yttrium iron garnet (YIG) [39](#bib.bib39). We excite the spin wave by sending a microwave current through a gold stripline on the YIG ([fig. 4](#S2.F4)(a)) under a static external magnetic field $B=$22\text{\,}\mathrm{mT}. The spin wave generates a microwave magnetic stray field that drives the NV spins when its frequency matches the NV ESR frequency. To create a spatial standing-wave pattern in the microwave field that we can image via the NV ESR contrast (SI), we apply an additional, spatially homogeneous reference field of the same microwave frequency using a wire above the chip 11, 23. We scan the beam parallel to the sample surface and perpendicularly to the beam axis (fig. 4(a)(b)), and measure the NV ESR contrast by switching on and off the microwave drive at the ESR frequency $f=$2.439\text{,}\mathrm{G}\mathrm{H}\mathrm{z}. The result shown in [fig. 4](#S2.F4)(c) images the spin-wavefront in 1D with a resolution limited by the beam width and beam-sample distance. The observed wavelength of $\lambda=$5.0\text{\,}\mathrm{\SIUnitSymbolMicro m} corresponds reasonably well with the $6\text{\,}\mathrm{\SIUnitSymbolMicro m}$ expected from the spin-wave dispersion (SI), given the uncertainty in the angle of the applied magnetic field.

3 Conclusion

To conclude, we demonstrated a new fiber-based approach for scanning NV magnetometry measurements. Using quasi-isotropic etching, we nano-fabricate diamond nanobeams out of single-crystal bulk diamond and couple them to tapered optical fibers. We read out ensemble NV signals through the fiber-nanobeam coupling with an estimated efficiency of 8.6(4)% at the coupling interface. As a demonstration, we show that our device can function as a scanning sensor to measure in 1D the planar spin wave in YIG.

A remaining challenge lies in increasing the control over the angle and position when attaching the nanobeam to the fiber. While we found that we can consistently break off the beams and attach them to a fiber, their relative position after the breaking process is not entirely under control due to the abrupt motion of the fiber-nanobeam when the tether breaks. We expect that reducing the tether width further, or reducing the nanobeam surface roughness via improved etching or ion-based polishing 36, could improve the coupling efficiency. Additionally, we found that transporting the fiber-nanobeam probe is challenging due to vibration and/or static electricity that cause the nanobeam to detach. Possible solutions could include coating the nanobeam/fiber to enhance the fiber-diamond adhesion, and transporting the device in a electrostatic-free environment such as a metal enclosure. Further steps towards 2D magnetic imaging (fig. 4(d)) include deterministically placing NV centers at the end of the nanobeams by e.g. pre-localizing NV centers 40 or deterministic implantation 41. With above mentioned efforts, our work holds potential for implementation in low-temperature setups with reduced heat load and easier alignment, opening another possibility for imaging weak magnetic effects at low temperature e.g. currents in quantum Hall devices 42 and Josephson junctions 43.

4 Methods

Magnetometry with NV centers

The NV center is a spin-1 system. The ground state of an NV center splits into three spin substates $m_{S}=0,\pm 1$, and the microwave-driven transition between $m_{S}=0$ and $m_{S}=\pm 1$ states can be detected via the photoluminescence intensity under non-resonant green laser excitation: Once the frequency of applied microwave matches the $m_{S}=0\rightarrow\pm 1$ transition frequencies (ESR frequencies), the photoluminescence emission of the NV center will decrease due to the higher non-radiative decay rate of the $m_{S}=\pm 1$ states. Applying an external magnetic field lifts the degeneracy of the $m_{S}=\pm 1$ states, allowing magnetic field measurement through measuring the ESR frequencies. More detailed information on the working principle of NV centers can be found in Refs. 1, 2, 3, 4.

Device Fabrication

We fabricate the diamond nanobeams on single crystal CVD diamond (Element-six DNV-B14) with ensemble NV centers generated during growth. Before fabrication, we mechanically polish the diamond surface down to $R_{a}\sim$2\text{,}\mathrm{n}\mathrm{m}$$ (Almax EasyLab) and clean the diamond chip with fuming nitric acid ($\mathrm{HNO_{3}}$).

To fabricate the beams, we first deposit a 200 nm layer of $\mathrm{Si_{3}N_{4}}$ on the surface with PECVD ($20\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$ $\mathrm{SiH_{4}}$/$20\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$ $\mathrm{NH_{3}}$/$980\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$ $\mathrm{N_{2}}$, deposited at $300\text{\,}\mathrm{\SIUnitSymbolCelsius}$, Oxford Instruments Plasmalab 80 Plus) as the hard mask. We then spin-coat a $\sim$400\text{,}\mathrm{n}\mathrm{m} layer of e-beam resist (AR-P 6200-13) and a $\sim$30\text{\,}\mathrm{n}\mathrm{m} conductive layer of Elektra-92 on top to write the pattern with e-beam lithography (Raith EBPG5200). We transfer the e-beam pattern from the resist to the SiN hard mask by an anisotropic ICP-RIE etch with CHF3/O2 (60\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$/$6\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}, $50\text{\,}\mathrm{W}$ RF and $500\text{\,}\mathrm{W}$ ICP at $20\text{\,}\mathrm{\SIUnitSymbolCelsius}$, AMS 100 I-speeder). We then remove the resist with dimethylformamide (DMF) and subsequent Piranha cleaning (96% H2SO4 and 31% H2O2, 3:1 mixed at $80\text{\,}\mathrm{\SIUnitSymbolCelsius}$). An ICP-RIE etch with O2 ($50\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$, $90\text{\,}\mathrm{W}$ RF and $1100\text{\,}\mathrm{W}$ ICP at $20\text{\,}\mathrm{\SIUnitSymbolCelsius}$, Oxford Instruments Plasmalab 100) transfers the pattern onto the diamond.

To protect the sidewalls of the structure during the subsequent undercut etch, we deposit $\sim$20\text{,}\mathrm{n}\mathrm{m} of $\mathrm{Al_{2}O_{3}}$ with ALD (280 cycles, at $105\text{\,}\mathrm{\SIUnitSymbolCelsius}$, Oxford Instruments FlexAL) and remove the $\mathrm{Al_{2}O_{3}}$ on the topside with another ICP-RIE with BCl3/Cl2 ($45\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$/$5\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$, $10\text{\,}\mathrm{W}$ RF and $600\text{\,}\mathrm{W}$ ICP at $20\text{\,}\mathrm{\SIUnitSymbolCelsius}$, Oxford Instruments Plasmalab 100). We do the final undercut of the beams with quasi-isotropic O2 ICP-RIE at $65\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($50\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$, $0\text{\,}\mathrm{W}$ RF and $2500\text{\,}\mathrm{W}$ ICP, Oxford Instruments Plasmalab 100). For the sample discussed in the main text, completely undercutting the $\sim$500\text{\,}\mathrm{n}\mathrm{m} wide nanobeams took 12 hours. The etch rate of our quasi-isotropic etching process is mainly limited by the maximum etching temperature of our system, and varies over different design, sample and etcher condition. All the masks are eventually cleaned with 40% hydrofluoric acid (HF, 10 min). Further details of the relevant recipe parameters can be found in Ref. 22.

We fabricate the tapered fibers by wet etching commercial optical fibers (S630-HP) with 40% HF. We dip one end of the fiber into the acid and pull it out at constant speed using a motorized translation stage (Thorlabs MTS25-Z8). The tapering angle can thus be controlled by tuning the pulling speed 15.

5 Author Information

5.1 Funding

This work is supported by the Dutch Science Council (NWO) through the NWA grant 1160.18.208 and the Kavli Institute of Nanoscience Delft. N.C. acknowledges support from the joint research program “Modular quantum computers” by Fujitsu Limited and Delft University of Technology, co-funded by the Netherlands Enterprise Agency under project number PPS2007.

5.2 Author Contributions

Y.L., R.N. and T.v.d.S. conceived the experiments. Y.L. and F.G. developed the measurement setup and performed the experiments. Y.L., R.N., N.C., S.G. and R.H. developed the diamond fabrication recipes and Y.L. fabricated the diamond nanobeam samples. S.K. prepared the YIG sample for the imaging measurements. Y.L. and T.v.d.S. analyzed the results. Y.L. and T.v.d.S. wrote the manuscript with contributions from all coauthors.

5.3 Notes

The authors declare no competing financial interest.

5.4 Data availability

All data plotted in the figures are this work are available at zenodo.org with identifier 10.5281/zenodo.7561825. Additional data related to this paper are available upon request.

{acknowledgement}

The authors thank T. Bredewoud for theoretical simulations of the fiber-nanobeam coupling, B.G. Simon, M. Ruf and C. van Egmond for the help in the fabrication process.

{suppinfo}

Estimation of coupling efficiency using the absorption cross section method; Explanation on the spin wave dispersion in YIG, and the principles of using NV centers to image propagating spin waves.